In recent years, holographic microscopes using digital holography are proposed variously for improving conventional optical microscopes (for example, refer to non-patent document 1). In the case of a usual optical microscope, it is necessary to adjust the focal distance of an image formation lens when the position of a viewpoint changes, because depth of focus of the usual optical microscope is very shallow. Accordingly, it is not so easy to observe a microscopic subject like a microbe etc. moving frequently in a three-dimensional space using the optical microscope. A holographic microscope can reconstruct (reproduce) a image of an observation object at an arbitrary focal distance by numerical computation using a recorded hologram in which a spatial distribution of amplitude and phase of an object light from the observation object is recorded with a photodetector. Moreover, since the holographic microscope can reconstruct the phase distribution of object light, it is applicable to quantitative analysis of a light transmission object.
By the way, a holographic microscope is classified roughly two: one uses an image formation lens inserted between a microscopic subject and a photodetector; and the other does not use such an image formation lens. A magnified three-dimensional image can be recorded as a hologram by magnifying a three-dimensional image of a microscopic subject in front of a photodetector using an image formation lens, and a high-resolution image is easily obtained from this record hologram. However, if an image is magnified using an image formation lens, the depth of recordable space will be restricted or the depth of focus of a magnified image will become shallow. Moreover, since some distortion and out-of-focus arises in an image magnified by the lens, a right-shaped image can not be obtained. Furthermore, a lens cannot usually be used as-it-is, for example, underwater which differ from air, since a lens functions according to refractive index difference to the air at lens boundary. That is, since an image formation lens of a microscope is designed on an assumption for observing a photographic subject in air or a photographic subject of thin thickness covered with a cover glass, if a photographic subject is in a deep position in water not in air, an image recorded through such a lens becomes an image with some distortion or out-of-focus.
Holographic microscopes using a spherical wave light, not using an image formation lens, are known (for example, refer to non-patent document 2 and patent document 1). These holographic microscopes are transmission type microscopes of Gabor type in-line holography and record interference fringe pattern between an un-scattered transmitted light and a scattered transmitted light caused by illuminating a photographic subject with one spherical wave light which spreads from a pinhole. Since these holographic microscopes record an object light with a large numerical aperture (NA) without using an image formation lens, a three-dimensional image of a microscopic subject existing in space with depth can be recorded as a hologram, and also can record a microscopic subject in a medium like water. Moreover, the patent document 1 discloses a method to reconstruct a distortionless image using an exact solution of Helmholtz equation in order to reconstruct a distortionless high-resolution image from a large numerical aperture hologram.